What effect of adding a Helmholtz Resonator to a cabinet?

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hi, did you come up with a satisfactory explanation why the same element can act as a sound energy booster but also as a sound energy absorber?

...and...

I know that, but that's not what I asked.

If you asked something else, then I don't get it. But maybe it's more a question of what you mean by the term "booster"?

Once the sound energy produced by the loudspeaker hits the Helmholtz resonator (HR), the sound energy at the HR resonance frequency tends to be trapped in the HR. In other words, the sound energy at this frequency is "sucked out" of the main loudspeaker box and is focused inside the HR. The HR does not increase the amount of energy in the loudspeaker system relative to the energy input to the system.

Is this what you mean by "booster"?
 
^A closed box system is a "mass-on-a-spring system", where the air acts as the spring that is coupled to the moving mass of the woofer (cone, voice coil, spider, surround, etc.). Increasing the volume of the box is equivalent to reducing the compliance of the spring (using "softer" spring).

The Helmholtz resonator itself is just another "mass-on-a-spring" system (mass of air in the port coupled to the air-"spring" enclosed in the Helmholtz resonantor).

Adding a Helmholtz resonator to a closed box would therefore be the same as coupling two mass-on-a-spring systems to each other. This is fundamentally different to increasing the volume of a closed box (=reducing the spring compliance in a simple mass-on-spring system).
 
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